We study the multiloop amplitudes of the light-cone gauge closed bosonic string field theory for $d eq 26$. We show that the amplitudes can be recast into a BRST invariant form by adding a nonstandard worldsheet theory for the longitudinal variables
$X^{pm}$ and the reparametrization ghost system. The results obtained in this paper for bosonic strings provide a first step towards the examination whether the dimensional regularization works for the multiloop amplitudes of the light-cone gauge superstring field theory.
We consider the dimensional regularization of the light-cone gauge type II superstring field theories in the NSR formalism. In the previous work, we have calculated the tree-level amplitudes with external lines in the (NS,NS) sector using the regular
ization and shown that the desired results are obtained without introducing contact term interactions. In this work, we study the tree-level amplitudes with external lines in the Ramond sector. In order to deal with them, we propose a worldsheet theory to be used instead of that for the naive dimensional regularization. With the worldsheet theory, we regularize and define the tree-level amplitudes by analytic continuation. We show that the results coincide with those of the first quantized formulation.
We study how the dimensional regularization works in the light-cone gauge string field theory. We show that it is not necessary to add a contact term to the string field theory action as a counter term in this regularization at least at the tree leve
l. We also investigate the one-loop amplitudes of the bosonic theory in noncritical dimensions and show that they are modular invariant.
We review our recent proposals to dimensionally regularize the light-cone gauge string field theory.
Light-cone gauge superstring theory in noncritical dimensions corresponds to a worldsheet theory with nonstandard longitudinal part in the conformal gauge. The longitudinal part of the worldsheet theory is a superconformal field theory called X^{pm}
CFT. We show that the X^{pm} CFT combined with the super-reparametrization ghost system can be described by free variables. It is possible to express the correlation functions in terms of these free variables. Bosonizing the free variables, we construct the spin fields and BRST invariant vertex operators for the Ramond sector in the conformal gauge formulation. By using these vertex operators, we can rewrite the tree amplitudes of the noncritical light-cone gauge string field theory, with external lines in the (R,R) sector as well as those in the (NS,NS) sector, in a BRST invariant way.
We propose a dimensional regularization scheme to deal with the divergences caused by colliding supercurrents inserted at the interaction points, in the light-cone gauge NSR superstring field theory. We formulate the theory in $d$ dimensions and defi
ne the amplitudes as analytic functions of $d$. With an appropriately chosen three-string interaction term and large negative $d$, the tree level amplitudes for the (NS,NS) closed strings can be recast into a BRST invariant form, using the superconformal field theory proposed in Ref.[arXiv:0911.3704]. We show that in the limit $d to 10$ they coincide with the results of the first quantized theory. Therefore we obtain the desired results without adding any contact interaction terms to the action.
Light-cone gauge NSR string theory in noncritical dimensions should correspond to a string theory with a nonstandard longitudinal part. Supersymmetrizing the bosonic case [arXiv:0909.4675], we formulate a superconformal worldsheet theory for the long
itudinal variables X^{pm}, psi^{pm}. We show that with the transverse variables and the ghosts combined, it is possible to construct a nilpotent BRST charge.
We study light-cone gauge string field theory in noncritical space-time dimensions. Such a theory corresponds to a string theory in a Lorentz noninvariant background. We identify the worldsheet theory for the longitudinal coordinate variables $X^pm$
and study its properties. It is a CFT with the right value of Virasoro central charge, using which we propose a BRST invariant formulation of the worldsheet theory.
